Data-Driven Koopman Controller Synthesis Based on the Extended $\mathcal{H}_{2}$ Norm Characterization

This letter presents a new data-driven controller synthesis based on the Koopman operator and the extended $\mathcal{H}_{2}$ norm characterization of discrete-time linear systems. We model dynamical systems as polytope sets which are derived from multiple data-driven linear models obtained by the finite approximation of the Koopman operator and then used to design robust feedback controllers combined with the $\mathcal{H}_{2}$ norm characterization. The use of the $\mathcal{H}_{2}$ norm characterization is aimed to deal with the model uncertainty that arises due to the nature of the data-driven setting of the problem. The effectiveness of the proposed controller synthesis is investigated through numerical simulations.